Robust m-estimator of parameters in variance components model

• Autorzy: Roman Zmyślony , Stefan Zontek
• Języki publikacji: EN

Abstrakty

EN

It is shown that a method of robust estimation in a two way crossed classification mixed model, recently proposed by Bednarski and Zontek (1996), can be extended to a more general case of variance components model with commutative a covariance matrices.

Słowa kluczowe

EN

Robust estimator; maximum likelihood estimator; statistical functional; Fisher consistency; Fréchet differentiability

Kategorie tematyczne

• 62J05: Linear regression
• 62F35: Robustness and adaptive procedures

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2002
• Tom: 22
• Numer: 1-2
• Strony: 61-71

Daty

wydano

2002

otrzymano

2002-11-26

Twórcy

autor

Roman Zmyślony

• Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Stefan Zontek

• Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [1] T. Bednarski, Fréchet differentiability and robust estimation, Asymptotic Statistics. Proc. of the Fifth Prague Symp. Physica Verlag, Springer, (1994), 49-58.
• [2] T. Bednarski, B.R. Clarke and W. Kokiewicz, Statistical expansions and locally uniform Fréchet differentiability, J. Australian Math. Soc., Ser. A 50 (1991), 88-97.
• [3] T. Bednarski and B.R. Clarke, Trimmed likelihood estimation of location and scale of the normal distribution, Australian J. Statists. 35 (1993), 141-153.
• [4] T. Bednarski and Z. Zontek, Robust estimation of parameters in mixed unbalanced models, Ann. Statist. 24 (4) (1996), 1493-1510.
• [5] B.R. Clarke, Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 11 (1983), 1196-1206.
• [6] B.R. Clarke, Nonsmooth analysis and Fréchet differentiability of M-functionals, Probab. Th. Rel. Fields 73 (1986), 197-209.
• [7] B. Iglewicz, Robust scale estimators and confidence intervals for location, D.C. Hoagling, F. Mosteller and J.W. Tukey, Eds., Understanding Robust and Exploratory Data Analysis, Wiley, New York, (1983), 404-431.
• [8] J. Kiefer, On large deviations of the empiric D.F. of vector chance variables and a law of iterated logarithm, Pacific J. Math. 11 (1961), 649-660.
• [9] D.M. Rocke, Robustness and balance in the mixed model, Biometrics 47 (1991), 303-309.
• [10] J. Seely, Quadratic subspaces and completness, Ann. Math. Statist. 42 (1971), 710-721.
• [11] R. Zmyślony and H. Drygas, Jordan algebras and Bayesian quadratic estimation of variance components, Linear Algebra and its Applications 168 (1992), 259-275.

Identyfikatory

DOI

10.7151/dmps.1032